Do you not like the idea that the GM may have to decide a mechanic to apply when a player comes up with an idea?
Do you prefer the mechanics always exist prior, so the the GM's job is more clearly defined in that he sets the DC (or at the very least consults the book to determine the DC)?
With reference to the first question, it depends what you mean by "deciding a mechanic to apply".
Here's an example that I don't mind at all (it's an actual play example from a game I GMed earlier this year): the PCs are driving across the surface of a desert planet in their ATVs, trying to avoid bombardment from a starship in orbit, with the fire being directed by a spotter flying above the surface in a small craft. The game (Classic Traveller) has rules for evasion of fire in a small craft, but no rules for evasion of fire in a ATV. I used the same rules, but substituted driving skill for piloting skill.
Here's an example that I'm not the biggest fan of, but it's the sort of thing I have to do quite a bit of in GMing the same system (Classic Traveller): when the players are attacking an enemy vessel, the players want their NPC ally with excellent computer skills to write some code that will jam the other ship's computer's targetting software, and transmit that via their communicators to that other ship. In a system like 4e or MHRP/Cortex+ Heroic this would be trivial to resolve, because they use "subjective" DCs in closed-scene resolution systems. But in Traveller this requires setting an "objective" DC, which helps establish the feel of the setting. Set it to low, and - even before one gets to issues of breaking the game - one can break the setting. Set it too high and one can break the players' engagement (and it's not like transmitting jamming signals seems out of place in a slightly pulpy sci-fi game). Burning Wheel also calls for a fair bit of this, but (a) has more examples of DCs in its skill descriptions, (b) is a fantasy game and so has less stuff that is anchored in the real world but draws on expertise I don't have, and (c) has many player-side metagame features that allow players to do stuff to maintain their engagement even when DCs are high or impossible (whereas Traveller has exactly zero of this sort of thing).
Here's an example I don't really like at all (it's from Moldvay Basic): the player, whose PC is losing a sword fight while standing on the edge of a cliff, and knowing that there is water somewhere in the dungeon below, declares "I jump over the edge hoping to land in a stream and survive!" Moldvay suggests that "there should always be a chance" and says the GM should work this out by thinking through the in-fiction logic of the situation: from memory, in this case he suggests a % roll with survival on 99 or 100.
I don't like that example because it requires me to, essentially, fiat the players chance of success (a) with no real mechanical guidelines or support as to what the chance should be, (b) not factoring in player-side resources or capabilities (such as PC DEX, in Moldvay's example; or WIS/Perception to perhaps hear the sound of running water from below), and (c) seemingly overriding both the extant falling damage system and the extant saving throw system.
The boundary between the second Traveller case and the Moldvay case is spectral, not sharp, but it's one that I feel nevertheless.
Here's quite a different example - this is another actual play one - and you may not regard it as falling under your question at all, but for me it does and I didn't really like it: in the Traveller game, before the PCs found themselves under bombardment, they were looking for a base out on the planet's surface (all the people on the planet live in a domed city - except for the sneaky ones who hang out in secret bases - and the PCs were trying to follow a vehicle that had left the city for the base). The game has encounter mechanics (which can also include results like getting lost), and rules for checking for vehicle failure; but it has no rules for working out when you get where you're going. (This is different from its interstellar jump rules, which are very solid in that respsect.) It assumes that the travel will be plotted on a map, but (at least in my view) that's not practical in a game where the PCs jump from planet to planet pretty often, and we're talking about on-world distances of hundreds or thousands of miles, and mapping correspondingly large areas; and also it gets very close to GM fiat, as my choice about where the base is, in a context where it only becomes salient because the PCs want to follow someone to it, becomes the overwhelming determinant of how the situation unfolds. I can't remember now exactly how I handled it, but think perhaps I rolled some dice to work out a distance (in days), and then used some Navigation-type checks on top of encounter results to determine how many extra days were taken. But the whole thing was unsatisfactory and fiat-laden. The contrast with a (somewhat) similar journey across a desert in a Burning Wheel game, which was easily resolved just by setting an Orienteering DC and then narrating an appropriate unhappy consequence when the check failed, was pretty marked.
Ultimately I want player choices to matter, and I want PC build to matter (eg having vehicle skill should make a difference when your PC is trying to achieve something using a vehicle) and - if the system uses dice - I want the dice rolls to matter. I don't like the GM's decision-making to be determinative, or even the predominant influence.
It's also not coincidence that all my examples are from Traveller, as it is the only system I've GMed in the past 10 or so years that doesn't have some sort of universal resolution system, and so it generates these issues in a way that those other systems (4e, BW, Prince Valiant, MHRP/Cortex+ are the main ones) don't. What I find amazing about Classic Traveller is how powerful it is as a system, despite some of the issues I've noted, given that it was designed in 1977 and it's rules are really pretty thin and it covers a pretty good spectrum of sci-fi action. I used to have more respect for Runequest than Traveller but I think that was a misjudgement.
If it's not GM input that you do not like, then what's the issue with the GM deciding what mechanic to apply based on the situation?
Hopefully I've answered this. I'm happy to say more if you're interested.
when rules are heavily codified, I think it does limit the players. There are plenty of anecdotes where a new player wows everyone at the table by coming up with some totally unexpected idea.
I can only speak about this from experience.
The first thing to say about that experience is that it includes very little 3E D&D - I mention that because for many posters on these boards that is an important comparison case - and that for the past 20 years it hasn't involved much open/club play. (That largely stopped when I finished my undergrad studies.)
But over the past 30 years, I've found that if a player's sheet tells them something encouraging about their PC's social capabilities, then they are more likely to declare interesting social actions than otherwise. I've also found that uncertainties across differing subsystems can make fair adjudicaiton hard. (An example that I can probably link to if you're interested: Luke Crane, in running Moldvay Basic, let someone move silently based on a DEX check - and only later on worke out that was proably hosing thieves who had a much lower % chance to move silently.) And I've found the best way to encourage players to declare interesting and unexpected actions is to adjudicate them fairly by reference to the mechanics so that the players know they can succeed (but perhaps also fail) and so they keep doing them (because they know they can succeed, although there is no guarantee).
No doubt others have had different experiences!
This happens because they don't know the rules. They don't know what they are allowed and not allowed to do. Creating a list of actions to add to an attempt at Influence/Diplomacy/Persuasion is limiting by its nature.
I think this may be how 3E handled it (I'm not sure - as I've said, it's not really a game where I'm across all the detail)?
I'm not a big fan of "allowed/not allowed". To me it's a product of class-based games with tightly circumscribed abilities (spell lists are a classic example but not the only one - thief abilities are another example, as Luke Crane belatedly realised!).
I prefer a system that allocates capabilities in ways that are mechanically fairly transparent, so that if you try strategy X rather than strategy Y you roughly know what you will be bringing to bear. In AD&D the way I got into this style of GMing was by refereeing an all-thief game - so (outside of magic, which is more easily quarantined within the context of the fiction) the issue of "that's not allowed" didn't really come up. (Maybe we had no tracking in that game - it was mostly city-based - or maybe someone had the Wilderness Survival Guide Tracking proficiency; I don't remember any more.) But for nearly 20 years (1990-2008) I overwhelmingly GMed Rolemaster, and it has an express "no limits, just costs" approach to PC building and making checks. Players naturally enough will try to steer the action into spheres of activity to which they're suited, but you will see them trying stuff that they need to try even if they're not too good at it.
And then 4e encouraged this sort of play even more because the "subjective" DCs within a skill challenge framework make success possible even for the poorly skilled, while allowing the specialists to be able to get the multiple successes within their field of specialisation that are needed to bring the situation to a successful conclusion. (Mathematically: a 50-50 chance of success is something that a player will attempt as a one-off to get something s/he wants; but that player can't win a skill challenge on 50-50 odds, so the "subjective" DCs don't lead to the unskilled "outshinging" the skilled in their field of expertise.)
In D&D, weapons and armor are more central than the finery of one's clothes. It's more important that the fighter is wearing plate armor than that the wizard is wearing a robe, or a scholar's outfit.
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As for powergaming and narrative approach, I think that Mearls meant that they focused more on narrative differences from character to character within the same class, rather than an overwhelming number of options in that class in order to differentiate. So instead of worrying about having a fighter subclass for each possible weapon type and so on, they said here are a few mechanical options, and here are others such as background, and bonds and flaws where you can make your fighter different from the other guys.
I don't think he's saying the sole way to differentiate is through these narrative means, nor is he describing D&D as a narrative game in the sense commonly used on these boards, but he's saying that the "options" that exist to create a unique character are more narrative based than they've been for D&D.
If the comparison class is D&D, as you suggest, then some of those remarks make more sense then they otherwise seemed to. Thanks for suggesting that reading.